4\frac{48}{72} + 3\frac{45}{72} + 5\frac{54}{72}
4\frac{8}{12} + 3\frac{10}{12} + 5\frac{9}{12}
4\frac{2}{8} + 3\frac{5}{8} + 5\frac{3}{8}
4\frac{16}{24} + 3\frac{15}{24} + 5\frac{18}{24}

Question

Accepted Answer

To determine which expression is equivalent (assuming we are looking for the one with the simplest or a common simplification, or maybe the one that sums to the same value, let's analyze each by simplifying the mixed numbers:

### First Expression: $ 4\frac{48}{72} + 3\frac{45}{72} + 5\frac{54}{72} $
Simplify fractions:
$ \frac{48}{72} = \frac{2}{3} $, $ \frac{45}{72} = \frac{5}{8} $? Wait, no, $ \frac{48}{72} = \frac{2}{3} $ (divide numerator/denominator by 24: $ 48\div24=2, 72\div24=3 $), $ \frac{45}{72} = \frac{5}{8} $ (divide by 9: $ 45\div9=5, 72\div9=8 $)—wait, no, $ 45\div9=5, 72\div9=8 $? Wait, $ 45\div15=3, 72\div15=4.8 $ no. Wait, $ 48\div24=2, 72\div24=3 $; $ 45\div9=5, 72\div9=8 $; $ 54\div18=3, 72\div18=4 $. Hmm, maybe not the simplest.

### Second Expression: $ 4\frac{8}{12} + 3\frac{10}{12} + 5\frac{9}{12} $
Simplify fractions:
$ \frac{8}{12} = \frac{2}{3} $, $ \frac{10}{12} = \frac{5}{6} $, $ \frac{9}{12} = \frac{3}{4} $. Not all with same denominator after simplification, but let's check the sum of the fractional parts: $ \frac{8+10+9}{12} = \frac{27}{12} = \frac{9}{4} = 2\frac{1}{4} $. Then the whole numbers: $ 4 + 3 + 5 = 12 $. Total: $ 12 + 2\frac{1}{4} = 14\frac{1}{4} $.

### Third Expression: $ 4\frac{2}{8} + 3\frac{5}{8} + 5\frac{3}{8} $
Simplify fractions:
$ \frac{2}{8} = \frac{1}{4} $, $ \frac{5}{8} $ (already simple), $ \frac{3}{8} $ (already simple). Sum the fractional parts: $ \frac{2 + 5 + 3}{8} = \frac{10}{8} = \frac{5}{4} = 1\frac{1}{4} $. Whole numbers: $ 4 + 3 + 5 = 12 $. Total: $ 12 + 1\frac{1}{4} = 13\frac{1}{4} $.

### Fourth Expression: $ 4\frac{16}{24} + 3\frac{15}{24} + 5\frac{18}{24} $
Simplify fractions:
$ \frac{16}{24} = \frac{2}{3} $, $ \frac{15}{24} = \frac{5}{8} $, $ \frac{18}{24} = \frac{3}{4} $. Wait, but sum the fractional parts: $ \frac{16 + 15 + 18}{24} = \frac{49}{24} = 2\frac{1}{24} $. Whole numbers: $ 4 + 3 + 5 = 12 $. Total: $ 12 + 2\frac{1}{24} = 14\frac{1}{24} $.

Wait, maybe the question is which one is simplified or which one has a common factor. Wait, the third expression: $ 4\frac{2}{8} + 3\frac{5}{8} + 5\frac{3}{8} $. Let's compute the sum:

Whole numbers: $ 4 + 3 + 5 = 12 $
Fractional parts: $ \frac{2 + 5 + 3}{8} = \frac{10}{8} = \frac{5}{4} = 1\frac{1}{4} $
Total: $ 12 + 1\frac{1}{4} = 13\frac{1}{4} $

Wait, maybe the third expression is the one with the simplest fractional parts (denominator 8, and numerators 2,5,3 which add to 10, simplifying to $ \frac{5}{4} $). Alternatively, maybe the question is which one is equivalent to a simpler form. Wait, maybe the third expression is the answer if we consider simplification (since $ \frac{2}{8} = \frac{1}{4} $, $ \frac{5}{8} $, $ \frac{3}{8} $, but when added, the numerators sum to 10, which is easy).

Alternatively, maybe the question is to find which expression is the simplest or has a common denominator that's easy. Let's check the third expression: $ 4\frac{2}{8} + 3\frac{5}{8} + 5\frac{3}{8} $. The fractional parts all have denominator 8, so adding the numerators: 2 + 5 + 3 = 10, so $ \frac{10}{8} = \frac{5}{4} $, and the whole numbers: 4 + 3 + 5 = 12, so total is $ 12 + \frac{5}{4} = 13\frac{1}{4} $.

If we assume the question is to identify the expression that is simplified or has the simplest fractional parts, the third one ($ 4\frac{2}{8} + 3\frac{5}{8} + 5\frac{3}{8} $) has the fractional parts with denominator 8, and numerators that sum easily.

So the answer is the third option: $ \boldsymbol{4\frac{2}{8} + 3\frac{5}{8} + 5\frac{3}{8}} $

# Brief Explanations:
To determine the correct expression, we analyze the simplification and sum of fractional parts:
- The third expression $ 4\frac{2}{8} + 3\frac{5}{8} + 5\frac{3}{8} $ has fractional parts with a common denominator (8), making addition of numerators (2 + 5 + 3 = 10) straightforward. Simplifying $ \frac{10}{8} = \frac{5}{4} $, and adding the whole numbers (4 + 3 + 5 = 12) gives a clear, simplified result. Other expressions have more complex or less uniform fractional simplifications.

# Answer:
$ 4\frac{2}{8} + 3\frac{5}{8} + 5\frac{3}{8} $ (the third option, with the checkbox next to $ 4\frac{2}{8} + 3\frac{5}{8} + 5\frac{3}{8} $)

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Question

Explanation:

First Expression: \( 4\frac{48}{72} + 3\frac{45}{72} + 5\frac{54}{72} \)

Second Expression: \( 4\frac{8}{12} + 3\frac{10}{12} + 5\frac{9}{12} \)

Third Expression: \( 4\frac{2}{8} + 3\frac{5}{8} + 5\frac{3}{8} \)

Fourth Expression: \( 4\frac{16}{24} + 3\frac{15}{24} + 5\frac{18}{24} \)

Answer: